Free Practice Question

PS · Problem Solving

655-705

Exponents/Powers

Given distinct positive integers p, q, r, and s such that $p^{q}=r^{s}$ , what is the minimum value of $p+q+r+s$ ?

Answer Choices

Correct answer marked below

A

10

B

11

C

12

D

13

14

Correct

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3

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A

AdityaJan 3, 2025

Thank you very much!

C

ChithiraJan 14, 2025

Greatt

A

ArunMar 9, 2024

Thank for sharing!

What this question tests

What it tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Common trap

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).

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Given distinct positive integers p, q, r, and s such that pq=rsp^{q}=r^{s}pq=rs, what is the minimum value of p+q+r+sp+q+r+sp+q+r+s?